Short story set in Larry Niven's Known Space Universe, or maybe in an alternate version of Known Space Universe. Has erroneuous dates..
In 2322 (2526), Skyhook Enterprises on Earth built the first safe ramscoop starship. The company was run by Douglas Hooker and partner Greg Loeffler. In 2353 (2557), Greg and his family emigrated to the colony of Plateau.
Douglas, a shy and lonely man, was left friendless. As a potential paranoid, he took anti-psychotic drugs regularly. But in 2366 (2570), malfunction of his desk doc stopped the drug therapy. Doug went murderously insane, blaming Greg for his unhappiness, and took off for Plateau in another starship. UN agent Loughery investigated the unauthorized takeoff, and sent a warning to Plateau.
Arriving at Plateau in 2379 (2583), Doug used his fusion drive to torch Greg's house. Greg escaped but his family was killed. Sonic hypnosis was used on Doug, forcing him to land. Nearly two years of psychotherapy followed, fully curing him of his insanity. Wanting to distance himself from Greg, Doug took off in his ship for the colony of Wunderland.
But Greg chased in his own ramscoop ship, and used a laser to attack Doug's ship. Greg had gone insane and wanted revenge. Doug responded with his own laser until Greg's laser quit, but was forced to keep fleeing ahead of the deadly magnetic field of Greg's ship.
The two ramscoop ships continued their chase at high relativistic speeds into the far distant future. Eventually Doug discovered his pursuer was dead; the lifesystem of Greg's ship had been destroyed by laser fire. But Greg's ship on autopilot continued the chase. Finally the ships edged too close and Doug was killed.
Published in Neutron Star.
Other sites: Known Space Concordance,